Title: Markov switching positive conditional mean models: Structure and examples
Authors: Christian Francq - CREST and University Lille III (France)
Abdelhakim Aknouche - Department of Mathematics, College of Science, Qassim University (Saudi Arabia) [presenting]
Abstract: A Markov-Switching autoregressive conditional mean model, valued in the set of nonnegative numbers, is considered. The conditional distribution of this model is a finite mixture of nonnegative distributions whose conditional mean follows a GARCH-like pattern with parameters depending on the state of a Markov chain. Three different variants of the model are examined depending on how the lagged values of the mixing variable are integrated into the conditional mean equation. The model includes, in particular, Markov mixture versions of various well-known nonnegative time series models such as the autoregressive conditional duration (ACD) model, the integer-valued GARCH (INGARCH) model, and the Beta observation-driven model. Under contraction in mean conditions, it is shown that the three variants of the model are stationary and ergodic when the stochastic order and the mean order of the mixing distributions are equal. The proposed conditions match those already known for Markov-switching GARCH models. We also give conditions for finite marginal moments. Applications to various mixture and Markov mixture count, duration, and proportion models are provided.